This is a worksheet I wrote to replace a lecture on introductory information about circles and tangents. In the past, I would incorporate most of this information into a lecture, and by the time I finished the lecture, there were just a few short minutes for the students to engage with the material.
Instead, I now spend the first 15-20 minutes of class giving the students a "mini-lesson" on what the main ideas are for the day: in this case, definitions of chords, diameters, secants, tangents, and the fact that tangent segments to a circle are congruent. Students also investigate the relationship between radii drawn to a point of tangency, and conclude the radius is perpendicular to the tangent line, which leads to right triangle problems.
I use this activity within cooperative groups, and I circulate to make sure they are getting the purpose of the questions.
The file includes spiral review problems.
This worksheet is intended to be written on directly.
Please download the pdf preview file first, so you can see exactly what's included; the product file is a word document, which you may personalize for your students.